Automated shape differentiation in the Unified Form Language

Ham, David A.; Mitchell, Lawrence; Paganini, Alberto; Wechsung, Florian

Abstract

We discuss automating the calculation of weak shape derivatives in the Unified Form Language (JAMA 40(2):9:1–9:37 2014) by introducing an appropriate additional step in the pullback from physical to reference space that computes Gâteaux derivatives with respect to the coordinate field. We illustrate the ease of use with several examples.

Citation

Ham, D. A., Mitchell, L., Paganini, A., & Wechsung, F. (2019). Automated shape differentiation in the Unified Form Language. Structural and Multidisciplinary Optimization, 60(5), 1813-1820. https://doi.org/10.1007/s00158-019-02281-z

• Journal Article Type: Article
• Acceptance Date: Apr 9, 2019
• Online Publication Date: Aug 2, 2019
• Publication Date: Nov 30, 2019
• Deposit Date: Aug 29, 2018
• Publicly Available Date: Aug 6, 2019
• Journal: Structural and Multidisciplinary Optimization
• Print ISSN: 1615-147X
• Electronic ISSN: 1615-1488
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 60
• Issue: 5
• Pages: 1813-1820
• DOI: https://doi.org/10.1007/s00158-019-02281-z
• Public URL: https://durham-repository.worktribe.com/output/1316055
• Related Public URLs: https://arxiv.org/pdf/1808.08083.pdf